The extended Schwarz's lemma, the maximum modulus theorem, and the structure of the zero sets defined in the newly constructed theory of regular functions and polynomials of a quaternionic variable are used to deduce the bounds for the zeros of these polynomials and regular functions. Our ...
38 MIN LEE_ AN EXTENSION OF VENKATESH’S CONVERSE THEOREM TO THE SELBERG CLASS 54:23 BENJAMIN SCHRAEN_ AROUND THE CLASSICALITY OF P-ADIC AUTOMORPHIC FORMS 56:22 JASMIN MATZ_ QUANTUM ERGODICITY IN THE LEVEL ASPECT 57:47 PIERRE COLMEZ_ ON THE P-ADIC ETALE COHOMOLOGY OF COVERINGS OF DRINFELD...
The authors give rather complicated lower bounds R 2 and R 4 , corresponding to R 1 and R 3 , producing annular regions R 2 ≤|z|≤R 1 (Theorem 1) and R 4 ≤|z|≤R 3 (Theorem 2) containing all the zeros of f. They claim that, in case k=0 or k=n-1, these give ...
摘要: If p(x) is nonnegative, monotonie and concave, no solution of y" + p(x)y = 0 has more than n + 1 zeros in the interval (a, b) defined by formula presented This is proved by showing that, if y'(a) =0, the nth succeeding zero of y'(x) will not precede b....
Intuitively, one would expect the sample complexity of error mitigation to scale with the size of the noiseless circuit \({{{\mathcal{C}}}\) and the amount of noise affecting it. Our Theorem 1 confirms this intuition starkly. It shows that the dependence of the resource requirement on the...
The Erdős-Ginzburg-Ziv constant of a finite abelian group G, denoted s(G), is the smallest k∈N such that any sequence of elements of G of length k contains a zero-sum subsequence of length exp(G). In this paper, we use the partition rank from [14], which generalizes the sl...
than any of the others, then it is the upper bound ofE. If, however, there is no such greatest number among the numbers ofE, this set may still have an upper bound. For example, the upper bound of all negative numbers is equal to zero. The set of all positive numbers is not ...
We prove Guerra's theorem, φ bounds and Frhlich bounds in the Y2 and φ34 field theories. Among our technical results of interest is a proof that Z ≠ 0 in φ34 and that the spatially cutoff vacuum in Y2 has a charge zero component. The... E.,Seiler,and,... - 《Annals of ...
An application of our main argument shows that, if M is locally free on the punctured spectrum of R, then either depth(MRN)≥depth(M)+depth(N)depth(R), or depth(MRN)≤codim(R). Along the way we generalize an important theorem of D.A. Jorgensen and determine the number of ...
the depth and size of the quantum circuits that can be executed, but also by the qubit connectivity of such devices2. Such processors have allowed for the first generation of quantum-technology demonstrations, ranging from experimental realizations of hybrid quantum-classical optimization techniques3,4...